Method to produce micro and nanofibers with controlled diameter and large yield

ABSTRACT

In one embodiment, the present invention is a method for producing microfibers comprising the steps of: (a) providing a base material; (b) forming the base material in a ring; (c) gripping opposing ends of the ring; (d) flipping one of the opposing ends relative to the other of the opposing ends, forming an upper portion and a lower portion; (e) folding the upper portion onto the lower portion; (f) stretching the folded upper and lower portions; and (g) repeating steps (d)-(f) as desired.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional under 35 U.S.C. § 121 of U.S. patentapplication Ser. No. 15/816,639, filed Nov. 17, 2017, which claims thebenefit of priority under 35 U.S.C. § 119(e) to U.S. Provisional PatentApplication Ser. No. 62/423,249, filed Nov. 17, 2016. The entire contentof each application is hereby incorporated by reference herein.

BACKGROUND OF THE INVENTION

Micro- and nanofibers have broad applications in the industry, spanningfrom traditional products, such as fabrics and textiles, to emergingproducts including biomedical materials, photovoltaic transducers andfuel cells. Application of micro- and nanofibers to non-woven fabricsalone produces $38 billion annual revenues, and is supporting more than160,000 jobs in the United States. The consumption of micro/nanofibersin the biomedical industry exceeded 30 metric tons in the year of 2012;this created a $24 million global market in 2012, and the market valueis projected to exceed $155 million by 2018 following a 36.8% compoundannual growth rate (CAGR). The global revenue of all products based onmicro- and nanofibers manufacturing is estimated to exceed $1 billion by2020. Micro- and nanofibers are used in medicine for artificial organcomponents, tissue engineering, implant material, drug delivery, wounddressing, and medical textile materials; in the military for bulletproof vests, sound absorption materials, infrared light absorbingtextiles, protective clothing against chemical and biological warfareagents, and sensor applications for detecting chemical agents; in thetextile industry for sport apparel, sport shoes, climbing, rainwear, andouterwear garments, baby diapers, napkins, non-woven fabrics; infiltration systems for HVAC (heating, ventilating, and air conditioning)filters, HEPA (high-efficiency particulate air) filter, ULPA (ultra-lowparticulate air) filters, air, oil, fuel filters for automotive, filtersfor beverage, pharmacy, medical applications, filter media for new airand liquid filtration applications, such as vacuum cleaners; and inenergy generation and storage for Li-ion batteries, photovoltaic cells,membrane fuel cells, and dye-sensitized solar cells, micropower tooperate personal electronic devices via piezoelectric nanofibers woveninto clothing, carrier materials for various catalysts, andphotocatalytic air/water purification.

In spite of the growing demands, the industrialization andcommercialization of micro- and nanofibers is hindered by the lack ofefficient manufacturing technique. Currently the production of micro-and nanofibers is mainly achieved by nozzle-based methods, includingelectrospinning, wet spinning, and thermal extrusion

In a platform of electrospinning, a fiber precursor is drawn intosubmicron-sized filaments by a high-voltage electric field. In general,a fiber material is pre-dissolved in a highly volatile solvent and formsa viscous solution. The solution is ejected through a nozzle (ex: aneedle head), and an electric field (in kilovolts) is applied betweenthe nozzle and an electrode plate. The electric field accumulatescharges and produces an electrostatic force between the nozzle andelectrode plate, and the electric force draws the fiber materials towardthe electrode plate, forming a stream of thin filament. The stream offilament dries quickly upon reaching the electrode plate, and forms asheet of fibers. The solution of fiber materials may be replaced with amelted polymer, which are heated above melting temperature upon ejectionand solidified on the electrode plate at a lower temperature. Thediameter of the as-formed fibers is determined by many factors,including nozzle size, feeding rate, material viscosity, materialconductivity, surface tension, electrodes voltage, charge density,melting point, and the hydraulic pressure for driving materials throughthe nozzle. Electrospinning is most suitable for making submicronsizedfibers, which have diameter ranged from one micron down to somewherebelow 100 nm.

In wet spinning, fiber materials dissolved in a solvent is injected intoan anti-solvent reservoir through a nozzle. The anti-solventprecipitates the materials, and turns the injected solution into afilament. A flow field is often created in the anti-solvent to helpcontrol the filament diameter, in which the force from flow may reducethe diameter of the injected stream. The filament diameter from wetspinning is determined by the nozzle size, feeding rate, materialviscosity, surface tension, and the intensity of flow in anti-solvent.The anti-solvent can be replaced by a chemical that fixes or crosslinksthe injected solution. In making calcium alginate fibers, for example, asolution of sodium alginate is ejected into a solution of calciumchloride, which turns alginate into hydrogel-based fibers. Wet spinningis suitable for making fibers that are thicker than 50 μm in diameter.

The mechanism of thermal extrusion is similar to wet spinning. Inthermal extrusion, a precursor is heated above the melting temperatureand ejected into cool air or a cooling liquid, which solidifies themelted materials. The fiber diameter from thermal extrusion isdetermined by nozzle size, feeding rate, material viscosity, and surfacetension.

For all the above nozzle-based methods, a rotating reel is sometimesinstalled to further reduce the diameter of micro/nanofibers. The reelhelps draw and thin the as-formed micro/nanofibers, while organizing thefibers into spools of bundles.

In spite of the efforts spent on developing micro/nanofibersmanufacturing, nozzle-based methods have the following challenges: (1)limited production rate, (2) difficulty in controlling fiber diameter,(3) challenges in producing aqueous-based fibers, (4) challenges toachieve fiber alignment and separation. Some reasons for theselimitations are follows.

A common limitation to the nozzle-based methods is their low productionrate on making ultra-thin fibers. Additionally, diameter control isessential to the performance of micro- and nanofibers. For example, inelectronics and optics applications, diameter affects the electricconductivity, mechanical elasticity, and refractive index of fibers,which in turn determine the device's functions. Diameter also affectsthe biomedical applications of micro- and nanofibers, as fiber sizedetermines the topographical signals, e.g. surface roughness,anisotropy, porosity and material diffusivity, that are presented toliving organisms, which influences the desired cell bioactivitiesincluding cell migration, cell proliferation, scar reduction, woundhealing and tissue regeneration.

Controlling the diameter of micro- and nanofibers is a formidable taskto the current technology. As mentioned above, in nozzle-based methodsfiber diameter is determined by the tight coordination among differentfactors including nozzle diameter, feeding rate, material viscosity,surface tension, voltage, charge density, melting point, and thehydraulic force that pumps the precursor through the nozzle. Identifyingthe optimal parameters to achieve a desired fiber-diameter is oftentime-consuming, and the optimum can be highly different betweendifferent materials.

Furthermore, most of the current manufacturing methods are suitable forfibers within a narrow size range. Electrospinning is suitable forproducing sub-micron sized fibers (100 nm to 1 μm), wet spinning for 50to 200 μm sized fibers, and thermal extrusion is more suitable forfibers thicker than 100 μm in diameter. Manufacturers therefore needdifferent platforms to cover different diameter ranges. Costs would bespent on multiple equipment setups, idle time, and personal training. Auniversal platform that covers a wide range of fiber diameter bysimplified procedures may dramatically save costs and acceleratemicro/nanofibers production.

Additionally, the nozzle-based methods demand tight coordination amongmanufacturing factors, and tolerate small variation in materialproperties, such as conductivity, viscosity and surface tension. It isparticularly difficult for the nozzle-based methods to turnaqueous-based materials into micro- and nanofibers, due to the fact thataqueous-based materials have much lower viscosity (<10 k-cps) and highersurface tension (>50 mN/m) in comparison with water-free material andare much more difficult to coordinate with other manufacturing factors.This issue has hindered the application of micro/nanofibers to thepharmaceutical industry, as aqueous-based materials, such as hydrogelsmade of a large variety of natural and synthetic polymers, areincreasingly used for biomedical products including wound dressingpatches, drug delivery vehicles, and the tissue fillers forreconstructive surgery.

Alignment of micro- and nanofibers is essential to certain devicefunctions. For electronics applications, the alignment of a bundle ofmicro/nanofibers determines anisotropy of conductivity, capacitance andinductance of the fibers component. For fuel cells and photovoltaicdevices that use fibers electrodes, fiber alignment may facilitatecharge separation and enhance the efficiency of the devices. Forbiomedical applications, aligned fibers provide topographic guidance tothe activities of living cells and promote the regeneration of lineartissues including muscles, tendons and nerves.

Rotary reel is used for all nozzle-based systems to collect andsimultaneously align fibers by constant rotation. In electrospinning,fiber alignment is often achieved by a duel electrode-plates system, inwhich two electrode plates collect the as-spun fibers in parallel whileorganizing them into a sheet of parallel filaments.

However, it remains highly challenging to align ultra-thin fibers(diameter <1 μm) using the traditional techniques. While electrospinningis suitable for making sub-micron fibers, electrospun fibers are proneto fusing together and forming a sheet, due the fiber annealing bysolvent residue. This problem has limited the application of sub-micronfibers to the industry, as many devices require fibers separation. Inbattery devices, for example, fibers isolation is often demanded foreffective charge separation. In tissue engineering products, fibersseparation is required to facilitate matrix permeability, cellmigration, nutrient transport and tissue ingrowth.

Alternative methods have been developed to circumvent the abovelimitations, but are still not satisfactory. Porogen leaching,anti-solvent precipitation, and supercritical-gas foaming were developedto mass-produce highly porous materials. Inside these porous materials,the porous microstructures resemble the topography of micro andnanofibers; however, these methods are incapable of diameter control,fiber alignment and fiber separation. Self-assembly of small molecule,e.g. amphiphilic peptides (short sequences of amino acids) has beencreated to produce submicron fibers with controlled diameter andchemical properties, but does not facilitate fiber alignment. Smallmolecule self-assembly of is also unsuitable for mass-production due tohigh costs for peptides synthesis.

BRIEF SUMMARY OF THE INVENTION

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter.

In one embodiment, the present invention is a method for producingmicrofibers comprising the steps of: (a) providing a base material; (b)forming the base material in a ring; (c) gripping opposing ends of thering; (d) flipping one of the opposing ends relative to the other of theopposing ends, forming an upper portion and a lower portion; (e) foldingthe upper portion onto the lower portion; (f) stretching the foldedupper and lower portions; and (g) repeating steps (d)-(f) as desired.

In an alternative embodiment, the present invention is a method forproducing microfibers comprising the steps of: (a) providing a basematerial; (b) forming the base material in an elongate shape; (c)gripping opposing ends of the base material; (d) folding the basematerial (e) stretching the base material; (f) repeating steps (d)-(e)as desired.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and constitutepart of this specification, illustrate the presently preferredembodiments of the invention, and, together with the general descriptiongiven above and the detailed description given below, serve to explainthe features of the invention. In the drawings:

FIG. 1A is a first schematic drawing showing a “stretch and fold” methodof forming micro and nano fibers according to an exemplary embodiment ofthe present invention;

FIG. 1B is a second schematic drawing showing a “stretch and fold”method of forming micro and nano fibers according to an exemplaryembodiment of the present invention;

FIG. 1C is a third schematic drawing showing a “stretch and fold” methodof forming micro and nano fibers according to an exemplary embodiment ofthe present invention;

FIG. 1D is a fourth schematic drawing showing a “stretch and fold”method of forming micro and nano fibers according to an exemplaryembodiment of the present invention;

FIG. 1E is a fifth schematic drawing showing a “stretch and fold” methodof forming micro and nano fibers according to an exemplary embodiment ofthe present invention;

FIG. 1F is a sectional view of the micro and nano fibers formedaccording to a first exemplary embodiment;

FIG. 1G is a sectional view of the micro and nano fibers formedaccording to a second exemplary embodiment;

FIG. 2A is a first photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 2B is a second photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 2C is a third photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 2D is a fourth photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 2E is a fifth photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3A is a first photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3B is a second photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3C is a third photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3D is a fourth photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3E is a fifth photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3F is a sixth photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3G is a seventh photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3H is an eighth photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 3I is a graph showing the diameter of the fibers formed throughoutthe process;

FIG. 4A is a first photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 4B is a second photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 4C is a third photograph showing fibers formed using the processshown in FIGS. 1A-1E;

FIG. 4D is a graph of the respective Young's Modulus of the fibers ofFIGS. 4A-4C that were formed;

FIG. 5A is a first set of photographs showing fibers formed using theprocess shown in FIGS. 1A-1E;

FIG. 5B is a second set of photographs showing fibers formed using theprocess shown in FIGS. 1A-1E;

FIG. 5C is a third set of photographs showing fibers formed using theprocess shown in FIGS. 1A-1E;

FIG. 5D is a graph showing a change of scaffold stiffness from day 0 today 28;

FIG. 6A is a first photograph of the fibers formed using the process;

FIG. 6B is a second photograph of the fibers formed using the process;

FIG. 6C is a third photograph of the fibers formed using the process;

FIG. 6D is a fourth photograph of the fibers formed using the process;

FIG. 6E is a fifth photograph of the fibers formed using the process;

FIG. 7A is a first schematic drawings showing a “Stretch-and-Fold”method of forming micro and nano fibers according to several exemplaryembodiments of the present invention;

FIG. 7B is a plurality of exemplary fiber core shapes;

FIG. 7C is a plurality of exemplary core compartments;

FIG. 8A is a schematic drawing showing a first step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 8B is a schematic drawing showing a second step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 8C is a schematic drawing showing a third step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 8D is a schematic drawing showing a fourth step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 8E is a schematic drawing showing a fifth step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 8F is a schematic drawing showing a sixth step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 9A is a schematic drawing showing a first step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 9B is a schematic drawing showing a second step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 9C is a schematic drawing showing a third step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 9D is a schematic drawing showing a fourth step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 9E is a schematic drawing showing a fifth step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 9F is a schematic drawing showing a sixth step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 9G is a schematic drawing showing a seventh step in a method offorming micro and nano fibers according to another exemplary embodimentof the present invention;

FIG. 10A is a photograph showing a machine used for forming micro andnano fibers according to another exemplary embodiment of the presentinvention;

FIG. 10B is a photograph showing the grippers of the machine of FIG.10A;

FIG. 10C is a photograph of a water bath used to provide buoyancy tocounter the effect of gravity on the rod;

FIG. 10D is a schematic drawing showing twisting of a rod;

FIG. 10E is a schematic drawing showing twisting of the rod of FIG. 10D;

FIG. 10F is a schematic drawing showing twisting of the rod of FIG. 10D;

FIG. 10G is a schematic drawing showing stretching of the rod of FIG.10D;

FIG. 10H is a schematic drawing showing folding and twisting of the rodof FIG. 10D;

FIG. 10I is a schematic drawing showing folding twisting of the rod ofFIG. 10D;

FIG. 10J is a schematic drawing showing stretching of the rod of FIG.10D;

FIG. 10K is a schematic drawing showing folding and twisting of the rodof FIG. 10D;

FIG. 11A is a schematic drawing showing a method of forming micro andnano fibers according to another exemplary embodiment of the presentinvention;

FIG. 11B is a schematic drawing showing a method of forming micro andnano fibers according to another exemplary embodiment of the presentinvention;

FIG. 12 is a graph comparing yield vs. fabrication time of conventionalspinning and the inventive method;

FIG. 13 is a schematic model of a gelatin core at 310/α seconds, where arepresents the strength of instability and was estimated to be 0.74according to experimental data;

FIG. 14A is a first illustration showing an exemplary strategy of usingthe cell-sized microfibers to control the mechanosensing of cells;

FIG. 14B is a second illustration showing an exemplary strategy of usingthe cell-sized microfibers to control the mechanosensing of cells;

FIG. 14C is a third illustration showing an exemplary strategy of usingthe cell-sized microfibers to control the mechanosensing of cells;

FIG. 14D is a fourth illustration showing an exemplary strategy of usingthe cell-sized microfibers to control the mechanosensing of cells;

FIG. 14E is a schematic drawing of cytoskeleton-derivedmechanotransduction;

FIG. 15A is a photo showing cell morphology and the activation of YAP;

FIG. 15B is a photo showing cell morphology and the activation of YAP;

FIG. 15C is a photo showing cell morphology and the activation of YAP;

FIG. 15D is a photo showing cell morphology and the activation of YAP;

FIG. 15E is a photo showing cell morphology and the activation of YAP;

FIG. 15F is a photo showing cell morphology and the activation of YAP;

FIG. 15G is a photo showing cell morphology and the activation of YAP;

FIG. 15H is a photo showing cell morphology and the activation of YAP;and

FIG. 15I is a graph representing the levels of YAP activation in eachgroup from FIGS. 15B, 15D, 15F, and 15H.

DETAILED DESCRIPTION OF THE INVENTION

In the drawings, like numerals indicate like elements throughout.Certain terminology is used herein for convenience only and is not to betaken as a limitation on the present invention. The terminology includesthe words specifically mentioned, derivatives thereof and words ofsimilar import. The embodiments illustrated below are not intended to beexhaustive or to limit the invention to the precise form disclosed.These embodiments are chosen and described to best explain the principleof the invention and its application and practical use and to enableothers skilled in the art to best utilize the invention.

Reference herein to “one embodiment” or “an embodiment” means that aparticular feature, structure, or characteristic described in connectionwith the embodiment can be included in at least one embodiment of theinvention. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment, nor are separate or alternative embodiments necessarilymutually exclusive of other embodiments. The same applies to the term“implementation.”

As used in this application, the word “exemplary” is used herein to meanserving as an example, instance, or illustration. Any aspect or designdescribed herein as “exemplary” is not necessarily to be construed aspreferred or advantageous over other aspects or designs. Rather, use ofthe word exemplary is intended to present concepts in a concretefashion.

Additionally, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or”. That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. In addition, the articles “a” and “an” as usedin this application and the appended claims should generally beconstrued to mean “one or more” unless specified otherwise or clear fromcontext to be directed to a singular form.

Unless explicitly stated otherwise, each numerical value and rangeshould be interpreted as being approximate as if the word “about” or“approximately” preceded the value of the value or range.

The use of figure numbers and/or figure reference labels in the claimsis intended to identify one or more possible embodiments of the claimedsubject matter in order to facilitate the interpretation of the claims.Such use is not to be construed as necessarily limiting the scope ofthose claims to the embodiments shown in the corresponding figures.

It should be understood that the steps of the exemplary methods setforth herein are not necessarily required to be performed in the orderdescribed, and the order of the steps of such methods should beunderstood to be merely exemplary. Likewise, additional steps may beincluded in such methods, and certain steps may be omitted or combined,in methods consistent with various embodiments of the present invention.

Although the elements in the following method claims, if any, arerecited in a particular sequence with corresponding labeling, unless theclaim recitations otherwise imply a particular sequence for implementingsome or all of those elements, those elements are not necessarilyintended to be limited to being implemented in that particular sequence.

The present invention aims to provide a new fabrication platform tomass-produce ultra-thin filaments. These filaments have a tunablediameter that can be adjusted from hundreds of microns down to less than100 nanometers. An automatic machine 100 is provided to implement thismethod and facilitate automatic manufacturing. As used herein, thefilaments are referred as “microfibers” and “nanofibers”, whereinmicrofibers are defined as the fibers thinner than 100 micrometer (μm),and nanofibers are fibers thinner than 100 nanometers (nm).

This present invention is directed to help micro/nanofibersmanufacturers overcome the above limitations, and fabricate micro- andnanofibers with the following features: (1) high yield, (2) low cost,(3) widely tunable diameter (from hundreds of microns to below 100 nm),(4) broad material variety, and (5) easy alignment and separation.

The present invention provides ultra-fine fibers by repeatedlystretching and folding a precursor 100 in the shape of a ring (FIGS.1A-1E). The ring is comprised of a core 102 and a sheath 104compartments, shown in the sectional view of FIG. 1F. The corecompartment 102 is the material for the micro/nanofibers, such as apolymer or a hydrogel, and the sheath compartment is made of a soluble,sacrificial material that keeps the core materials aligned and separatedduring fabrication. After stretching and folding the ring (precursor100) for a certain number of times (n), the sheath compartment 104 isdissolved by a solvent, and fibers are retrieved from the core 102.Folding and stretching the precursor ring 100 by n times exponentiallyincreases the number of the cores 102 (N=2^(n)), while exponentiallydecreasing the diameter of the cores 102 (D=D₀/2^(0.5n)). FIG. 1F showsa sectional view of ring 100 after one fold and FIG. 1G shows asectional view of ring 100 after two folds. Accordingly, one can easilytune the diameter of micro-/nanofibers by adjusting the number ofstretch-and-fold cycles, while producing the fibers at a high speed.Using the inventive method, it can take less than 5 minutes to decreasethe core diameter from 5 mm to 200 nm, for which the number of foldingis 24.

To help implement the inventive stretch- and fold method for theindustry, a machine was developed to conduct the stretch- and foldprocedures automatically. Designs and prototypes for this machine 200will be described later herein.

In the first embodiment of the stretch-and-fold method, a ring-shapedprecursor 100 made of porcine gelatin (for core 102) andpolycaprolactone (PCL) (for sheath 104) was produced, and through thestretch-and-fold procedure the precursor 100 was converted into gelatinmicro and nanofibers (FIG. 1). The diameter of core gelatin fibers wastuned from about 100 microns to below 100 nanometers by increasing thenumber of stretch-and-fold cycles from 10 to 28, and released the corefibers 102 by dissolving the PCL sheath 104. The stretch-and-foldprocedure reduces the diameter of the core fibers exponentially;therefore the production rate of micro and nanofibers is extremelyhigher than any of the existing manufacturing methods. Such productionrate is not determined the quantity of material; a larger yield can beachieved by starting the stretch-and-fold procedure with a largerprecursor ring 100. Following are experimental details.

Prepare Gelatin Solution

To prepare the gelatin for microfiber fabrication, gelatin from porcineskin (Sigma-Aldrich, Cat #1890) was dissolved in pure water at 50 wt %and stirred at 100 rpm on a hot plate at 70° C. After the gelatin powderwas fully dissolved, the gelatin solution was centrifuged at 50° C. for10 minutes to remove air bubbles.

Encapsulating Gelatin PCL Ring and the Stretch-and-Fold Procedures

A ring-shaped precursor is prepared as follows. Polycaprolactone (PCL)pellets (50 g) were melted in a bath of olive oil at 75° C. Afterbecoming transparent and plastic, the clump of PCL was removed from theoil bath and molded into a tube with 5 mm internal diameter (ID) and 20mm external diameter (OD). The PCL tube became opaque and solidifiedafter cooling by air at room temperature. The gelatin solution obtainedin the previous step was injected into the PCL tube using a 25 mLsyringe. The ends of the PCL tube were sealed by melted PCL to containthe gelatin solution.

To conduct stretch-and-fold procedures, the PCL tube, now with a core ofgelatin, was heated in a 75° C. water bath with constant rolling. Uponexceeding the glass transition temperature of PCL (>60° C.), the PCLtube became plastic and accessible to stretching and folding. To form aPCL ring, the ends of the PCL tube were joined together as shown in FIG.1A. Immediately after this step, the ring was repeatedly stretched andfolded (FIGS. 1B, C and D), thinning the gelatin cores, until thedesired core diameter is reached. The stretch-and-fold procedure wasconducted swiftly in the ambient air before the PCL solidified. Thefolded PCL ring was immediately cooled and solidified at roomtemperature.

Retrieve Gelatin Micro/Nanofibers from PCL

To retrieve micro/nanofibers, the stretched-and-folded PCL ring was cutinto 5 to 8 cm segments, and dissolved by acetone at 30° C. under mildagitation, which released the gelatin core fibers (FIG. 2A to 2B).As-retrieved fibers were rinsed by fresh acetone at 30° C. for fivetimes to remove PCL residue (30 minutes each time). The resulting fiberswas fixed in glutaraldehyde solution (0.1% in methanol) for three hours,neutralized in lysine solution (1% in methanol), dialyzed againstdistilled water for 3 days, and finally freeze-dried for storage. Thediameter of core fibers was adjustable by the number of stretch-and-foldcycles (FIG. 2C), and can be tuned from hundreds of micron down tosub-micron, following a simple equation: D_(n)=D₀/2^(0.5n)

where n the number of stretch-and-fold cycles, Do is the original corediameter before folding, and D_(n) is the core diameter after nstretch-and-fold cycles.

Obtain Aligned Micro/Nanofibers

One major advantage of the stretch-and-fold method is the ease to obtainaligned fibers, since the PCL sheath maintain the linear organization ofcore fibers throughout stretching and folding. To maintain themicro/nanofibers alignment, clips 110 were used to constrain the corefibers at the ends of the PCL segments (FIG. 2D), before followingthrough the above protocols. This method produces a bundle of alignedmicro/nanofibers (FIG. 2E).

Measure Fiber Diameter by Fluorescent and Scanning Electron Microscopy

Gelatin micro/nanofibers have wide biomedical application. The diameterof gelatin fibers influences the efficiency of biochemical reaction,nutrient and mass diffusion, and the cellular responses to themicroenvironment following mechanosensing. This mechanism has been shownto dictate the outcome of bone healing by adipose derived stem cells.

To verify the effect of stretch-and-fold cycles on fiber diameter, thePCL ring with different cycles were cut into slices, fluorescentlystained for gelatin at the cross-section, and imaged to measure thecores diameter (FIG. 3A to 3D). The cores diameter was also measured onthe as-formed fibers using scanning electron microscope (SEM) (FIG. 3Eto 3H). The fiber diameter at the 10th stretch-and-fold cycle was about50 microns. Upon the 24th cycle, the average fiber diameter became 400to 500 nanometer. At the 28^(th) cycle, the average fiber diameter fellbetween 100 and 200 nanometer. Results from the measurementsdemonstrated that the fiber diameter underwent an exponential decreaseas the number of stretch-and-fold cycles linearly increased (FIG. 3I).

Smallest Available Diameter Depends on the Speed of Stretch-and-Fold

The smallest fiber diameter achievable by the stretch-and-fold method isdetermined by the following factors: (1) viscosity of the core material,(2) viscosity of the sheath material when heated above the glasstransition temperature; (3) surface tension at the interface between thecore material and the sheath material above glass transitiontemperature; and (4) the speed of stretch-and-fold procedure.

The Theory of Rayleigh-Plateau Instability predicts that, as the corediameter gradually decreases following stretching and folding, thesurface tension at the sheath-core interface will eventually overcomethe viscosity of sheath/core materials, and break the core fibers intobead-like segments. This phenomenon resembles the breakup of a stream oftap water, in which the core resembles water and the sheath materialresembles air.

The inventors discovered that that the effect of Rayleigh-PlateauInstability on the core compartment can be arrested by using sheath/corematerials of higher viscosity, or by accelerating the stretching andfolding cycles. Higher viscosity for sheath/core material can beobtained by using gelatin and PCL of higher molecular weight.

On the other hand, a faster stretch-and-fold procedure guarantees thatthe process of core thinning can be finished before the core start tobreakup via Rayleigh-Plateau Instability. In one embodiment, theinventors found that continual, 100-200 nm nanofibers made of gelatincan be produced via 28 stretch-and-fold cycles when the followingconditions were met:

(1) Use medium-molecular-weight (˜50,000 Da) PCL for the sheath.

(2) Use 50% w-w, 300 boom porcine gelatin for the core, and

(3) Complete the stretch-and-fold cycles in less than 10 minutes, thenimmediately cool the precursor to room temperature.

In contrast, when the above conditions (1) and (2) were met, but thetime for stretching-and-folding procedure increased to more than 20minutes, the maximum achievable number of stretch-and-fold cycles was 14(forming 15-20 micron fibers); beyond the 14th cycle the core started tobreak into microparticles instead of maintaining the filament shape:

(1) Medium-molecular-weight PCL for the sheath.

(2) 50% w-w, 300 boom porcine gelatin for the core.

(3) Complete the stretch-and-fold cycles in more than 20 minutes, thenimmediately cool the precursor to room temperature.

Since the speed of stretch-and-fold is essential to the continuity ofmicro/nanofibers, an automatic stretch-and-fold machine would be mostdesirable to manufacturers. This machine may accelerate thestretch-and-fold cycles, provide more repeatable results, and helpeliminate the effects of Rayleigh-Plateau instability.

Tuning Fiber Elasticity

Elasticity is another important factor for the function ofmicro/nanofibers, and is especially crucial to biomedical applications.For tissue fillers and wound dressers, the elasticity ofmicro/nanofibers determines the biophysical signals that cells sensefrom the product, which in turn affects the pace of wound healing andthe formation of different tissue types through cell-mechanosensing.Matrices softer than 1 kPa in Young's modulus were shown to promote fattissue formation, as matrices harder than 50 kPa shown to promote boneformation.

Elasticity of fibers produced by stretching-and-folding is determined bythe crosslinking of core compartment. In our first embodiment, fibercrosslinking was achieved by using glutaraldehyde (0.1% in methanol, 3hours), which crosslinks porcine gelatin rapidly by binding lysinecroups. The elasticity given by glutaraldehyde treatment can be tunedfrom 0.1 kPa to 20 kPa, as higher glutaraldehyde concentration andlonger treatment produce higher elasticity. To enhance the mechanicalproperty of fibers, glutaraldehyde can be replaced or added with othercrosslinking chemical, such as 1,4-butanediol diglycidyl ether andmethacrylate.

In comparison with glutaraldehyde, 1,4-butanediol diglycidyl ether(BDDE) is a slower crosslinker, but the slower reaction enables moreuniform BDDE diffusion and enhances the mechanical homogeneity offibers. The following steps are added to the protocol described above ifBDDE is used instead of glutaraldehyde:

(1) Add 0.01% to 1% BDDE to the gelatin solution, which crosslinksgelatin via lysine function groups. Glycidol at higher concentrationleads to higher Young's Modulus.

(2) Omit the use of glutaraldehyde.

(3) Before retrieving the core fibers from PCL, treat the as-folded PCLring in 50% oil bath for 24 hours. The heating acceleratesglycidol-crosslinking.

Methacrylate groups form the stiffest matrix in comparison withglutaraldehyde and BDDE, and can significantly increase the range ofYoung's Modulus. The following steps are added for methacrylatebasedcrosslinking:

(1) After retrieving the core fibers from PCL, rinse the fibers inmethanol with 1% to 20% methacrylate anhydride for 30 minutes at roomtemperature. This introduces methacrylate groups to gelatin via lysinegroups.

(2) Use glutaraldehyde as described above.

(3) Crosslink methacrylate groups before freeze-drying: rinse the fibersin water containing 0.05% phenyl-2,4,6-trimethylbenzoyl-phosphinate(LAP), expose the fibers to ultraviolet light (4 mW/cm²) for 10 minutes,then wash the fibers twice by distilled water. Methacrylate crosslinkingleads to a final Young's Modulus of 10 to 100 kPa, which is tunable bychanging the concentration of methacrylate anhydride in step (1)immediately above.

Independent Control of Fiber Elasticity and Diameter

Since elasticity and diameter are both important to the performance ofmicro/nanofibers, decoupled and independent control of these parameterswould be highly desirable to the manufacturers. To verify whether fiberdiameter and elasticity can be independently tuned, microfibers producedwith different diameters (via different stretch-and-fold cycles) but theconstant crosslinking density (BDDE) were prepared following the aboveprotocol. The fiber diameter was measured by using SEM, and the fiberelasticity was measured by nano-indentation based on atomic forcemicroscope (AFM).

Nanoindentation was carried out via a Dimension Icon AFM (BrukerNano,Santa Barbra, Calif.) under physiological-like conditions (PBS, ionicstrength≈0.15 M, pH 7.4, indentation rate≈10 μm/s). Custom-madeborosilicate microspherical tips with radii comparable to the size ofas-manufactured fibers (nominal spring constant k≈0.2 N/m) were used tosimulate the micromechanical force that living cells sense. At eachindentation location, the force versus depth (F-D) curves werequantified through an established calibration procedures. In themeantime, contact mode imaging was performed with the same tip underminimized compressive force (˜1 nN) to quantify the fibers 3Dtopography, i.e. thickness t, following an existing protocol. Effectiveindentation modulus, E_(ind), was calculated by applying linear elasticHertz model to the loading portion of each F-D curve. Substrateconstraint effects due to finite thickness t was corrected byF=4E_(ind)R^(1/2)D^(3/2)χ/[3(1−ν_(P) ²)] where ν_(P) is the Poisson'sratio (≈0.49 for highly swollen hydrogels), and χ the substrateconstraint correction factor (negligible when thickness >10×maximum ofD). In all measurement, the maximum indentation depth, D_(max), was made<500 nm (<20% local strain) to minimize material mechanicalnonlinearity. At Dmax, the maximum tip-sample contact radius is ≈2 μm,and thus, spatial maps of Eind was obtained at this resolution of ≈2 μmthrough controlling the close-looped X-Y piezo-stage of the AFM.

The results from nanoindentation showed that the fiber elasticity wasconsistently 110±10 kPa regardless of varying fiber diameter (FIG. 4).This result verifies that the stiffness and diameter ofstretched-and-folded fibers can be independently controlled by thecrosslinking density of the core compartment and the number ofstretch-and-fold, respectively.

Advantages of Stretch-and-Fold Method in Comparison with ExistingTechniques

Micro- and nanofibers are traditionally fabricated by nozzle-basedmethods, such as electrospinning, wetspinning and thermal extrusion.These methods have the production rates that decrease exponentially asthe fibers become thinner, are difficult to use for controlling fiberdiameter, and tolerate small variations in material properties, such asmelting point, material conductivity, electric permeability andviscosity.

These methods are prone to low yield, high cost, and limited materialoptions in making micro- and nanofibers. In contrast to the existingtechniques, the inventive stretch-and-fold platform provides uniqueadvantages as follows:

(1) Ease for Mass Production: In contrast to the nozzle-based methods,the stretch-and-fold method is based on cycles of stretching and foldingand suitable for mass-production. The production rate of the stretch-and fold method is insensitive to the diameter of micro/nanofibers,since the fiber diameter can be rapidly reduced, in several minutes,from hundreds of micron to below 100 nm. A larger production rate can beachieved by starting the stretch-and-fold protocol with a largerprecursor.

(2) Easily Customizable Fiber Diameter: In this invention the fiberdiameter is controlled by the number of stretch-and-fold cycles, and canbe easily customized to meet consumers' requirements. By simplyincreasing the number of stretch-and-fold cycles, the fiber diameter canbe tuned from hundreds of micron down to below 100 nm. In contrast,changing fiber diameter in the traditional methods often demand acomplex re-coordination among multiple factors, such as voltage,temperature, nozzle size, polymer density, extrusion speed, and the typeof solvent(s) being used. Such optimization demands extra labors,materials and cost, and has to be redone for every new material.

(3) Versatile Materials and Broad Applications: The principle of stretchand fold procedure is based on the pseudoplasticity of sheath materials,and is not based on the property of the core materials that form fibers.Choices for fiber material are therefore highly versatile and canincorporate different polymers, metals and metallic oxides of variousphysical and chemical properties. The stretch-and-fold fibers are usefulfor many applications. Micro/nanofibers of highly resilient polymers maybe used for body armor. Fibers made of photovoltaic polymer ormetallic-oxides may be used for solar plates. For biomedicalapplications, the stretch-and-fold method can be used to producehydrogel-based fiber for wound dressing, or engineering a broad varietyof tissue types such as of muscles, cartilage, bones and blood vessels.The inventive stretch-and-fold method has been used to produce micro andnanofibers from different hydrogels including gelatin, chondroitinsulfate and hyaluronic acid.

(4) Ease for Fiber Alignment: Alignment of micro- and nanofibersdetermines the fibers' anisotropy of conductivity, capacitance andinductance, and is crucial to the charge-separation for fuel cells andphotovoltaic devices. Aligned fibers also provide topographic guidanceto biological cells and promote the healing and regeneration of lineartissues, including muscles, tendons and nerves. However, alignment ofultra-thin fibers remains highly challenging due to the effect of fiberannealing associated with the existing techniques. In this invention,micro and nanofibers are automatically aligned by the stretch-and-foldprocedure, while being isolated by the sheath compartment. Bundles ofseparated, aligned micro/nanofibers are produced upon the removal ofsheath compartment.

Application Examples

The following examples demonstrate the potential applications ofstretch-and-fold fibers.

Application I: Tissue-Engineering Scaffolds for Cartilage Repair

The stretch-and-fold method has been applied to the regeneration ofcartilage tissue. The experiment was conducted using gelatin microfibersby the stretch-and-fold method, along with human mesenchymal stem cellsthat are capable of producing cartilage-like tissues.

Micro/nanofibers has gained great popularity as a biomaterial for tissueengineering. For healing muscles, nerves and tendon tissue, for example,aligned micro- and nanofibers may provide the biophysical cues forguiding cell alignment and tissue growth. On the other hand, non-alignedfibers can provide a highly porous space for cell spreading, migrationand proliferation in 3D, which promotes the regeneration of bones,cartilage and fat tissues. However, prior approaches to fabricate micro-and nanofibers, such as electrospinning, thermal spinning and wetspinning, are often limited due to the difficulty in controlling fiberdiameter, small variety of suitable materials, long fabrication time,and low production rate.

Furthermore, it is difficult to create micro- and nanofibers usinghydrogels, which are major biomaterials for regenerative medicine. Toovercome those limitations, the inventors have developed the presentmethod to mass-produce micro- and nanofibers using stretching andfolding. This technique is designed for creating micro- and nanofibersby a clinical-relevant quantity, and is especially suitable for makinghydrogel-based fibers. To verify the potential for tissue engineering,human mesenchymal stem cells (hMSCs) were encapsulated in hand-spunmicrofibers (2 microns in diameter) for chondrogenesis study.Preliminary results showed uniform cell distribution, cartilage-likeextracellular matrix (ECM) formation, and significantly increasedmechanical property in the microfiber-based scaffolds.

Scaffolds preparation. Gelatin fibers were produced through repeatedlystretching and folding a polymer ring that encapsulates gelatin (FIGS.1-1%1). The ring had a core-sheath structure, the sheath was made bypolycaprolactone (PCL) and the core was 50% porcine type-A gelatin inwater. After stretching and folding for desired number of cycles, fiberswere retrieved by dissolving the PCL sheath in acetone.

As-collected fibers were methacrylated, aldehyde fixed, and freeze-driedfor storage (following the protocol for methacrylate-crosslinking asdescribed above). For scaffold formation, the fibers were rehydrated,mixed with cells and finally crosslinked by UV exposure.

hMSCs were encapsulated in scaffolds at a density of either 5 or 10million cells per cm³, and cultured in chondrogenic media containingTGF-ß3 for 28 days. Mechanical testing, histology and immunofluorescencewere conducted from day 0 to day 28 for each group.

The diameter of stretched-and-folded fibers is determined by the numberof stretch-and-fold cycles. 20 cycles of stretch-and-fold led tocell-sized fibers (˜5 μm-thick), as 14-cycles led to fibers much largerthan cells (50 μm-thick fibers). Increasing the cycles number to 26 ledto nanofibers that are about 500 nm in diameter (FIG. 5A). The totaltime for stretch-and-fold procedure took less than 20 minutes,regardless of the quantity and diameter of micro- or nanofibers. Forchondrogenesis study, the macroporosity of scaffolds was determined byfiber diameter: 5 μm fibers produced 10 to 20 μm macroporosity, as 50 μmfibers produced macropores up to 200 microns. Cartilage-based ECMcontent, including type-II collagen, increased significantly within 28days and signified the progress of cartilage-like tissue formation (FIG.5B and FIG. 5C). The scaffold macroporosity supported the diffusion ofcell-produced ECM and dramatically increased the mechanical property ofscaffolds. The stiffness of scaffolds increased from 50 up to 220 KPa,approaching 25% of native cartilage within four weeks. (FIG. 5ED)

The inventive to produce micro/nanofibers was verified the potential ofthe microfibers for tissue engineering using a chondrogenesis study.Results showed that the microfibers support cell engraftment,chondrogenesis, ECM penetration and cartilage-like tissue formation.

Application II: Aligned Microfibers for Linear Tissue Engineering

To promote desired cell fates and tissue-formation, efforts have beenmade to create tissue-engineering scaffolds with customizedmicrostructures that mimic the extracellular matrix (ECM) in the humanbody. Aligned microfibers are promising for linear tissue formation,such as muscle, nerve, and layers of skin. Diameter of fiber determinesthe spatial guidance for cell spreading, cytoskeleton organization, andcell mechanosensing that triggers proliferation and celldifferentiation.

Prior methods to fabricate aligned microfibers include electrospinning,wet spinning, and macromolecular self-assembly. However, these methodsoften have difficulty in controlling fiber diameter, due to the limitedtunability in fabrication conditions. Prior methods are also challengedby the needs for high production rate, and tend to become extremely slowwhen producing sub-micron scale fibers. Furthermore, aligned fibersproduced by existing methods are often difficult to cellularize in 3D,due to the fact that the fibers can easily adhere with each other uponproduction, leaving insufficient space for cell diffusion.

The inventive “stretch-and-fold” method mass-produces microfibers withlinear alignment and easily customizable diameter. The method enables awidely tunable fiber diameter and extremely high fiber production rate.By stretching and folding a ring of porcine gelatin, aligned gelatinfibers with desired diameter can be easily produced. This methodprovides microfibers with aligned fibrous microstructures, whichfacilitates uniform cell distribution and cell spreading in 3D.

Aligned microfibers were obtained by repeatedly stretching and folding aring of porcine gelatin (50% in water). (FIG. 6A). Within N cycles, thelength of the fiber rapidly increased by 2N folds of the originalgelatin ring length, the diameter of the fiber decreases by 2N/2 folds,while a bundle of microfibers being formed. PCL was coated on thegelatin ring to keep the microfibers separated from each other duringstretching and folding. Microfibers were retrieved by dissolving the PCLwith acetone, while the alignment of the fibers was maintained byclipping the ends of fibers (FIGS. 6a -6B). As-produced fibers weremethacrylated, glutaraldehyde-fixed, washed and finally freeze-dried forstorage. To verify biocompatibility and the efficacy of 3D cell-culture,hMSCs were mixed among the microfibers (which were dissociated from eachother and allowed uniform cell distribution), and the microfibers werecrosslinked by light (365 nm, 4 mW/cm², 5 min) to become a 3D scaffold.(FIG. 6C) Cell attachment and spreading was monitored using fluorescentmicroscope.

This method is able to produce nanofibers less than 200 nm in diameter,if the 28 stretch-and-fold cycles are conducted. Resulted fibers possesshigh diameter uniformity and maintained alignment (FIG. 6D). Thestiffness of the microfiber can be adjusted from 10 kPa to 200 kPa, asquantified by AFM, by tuning the dose of glutaraldehyde and methacrylateanhydride. From cell study, fluorescent imaging demonstrated thespreading of hMSCs along the stretched-and-folded microfibers (˜10 umdiameter, 18 stretch-and-fold cycles), and the uniform cell distributionwithin the 3D microfiber-based scaffold. See FIG. 6F. The above resultsdemonstrate the potential of our stretched-and-folded micro/nanofibersfor regenerative medicine.

The inventive method mass-produces pre-aligned microfibers as tissueengineering scaffold. The hand-spinning protocol facilitatesmass-production and the easy control of fiber diameter. The fiberdiameter can be tuned, by the number of stretch-and-folding cycles, fromhundreds of microns down to less than 100 nm. Well-separated microfibersenable uniform cell distribution and encapsulation. These microfiberscan be widely useful for engineering linear tissues, such as muscles,tendons and nerves.

The above embodiments verify the efficacy of the stretch-and-fold methodon micro/nanofiber production and biomedical applications. However, thenature of stretch-and-fold method is not limited by these embodiments.

Materials for the core 102 and the sheath 104 of precursor 100 are notlimited to porcine gelatin and PCL. Any deformable materials (liquid,plastic or pseudoplastic) can be used as the core material, and anythermoplastic, plastic or pseudoplastic materials can be used as thesheath material. Besides polymers, the core and sheath materials canalso be an inorganic material, such as metals or metallic oxides.

Alternative materials for the core of precursor are list below:

Core Material Category Material Conditions for Stretch and FoldProcedure Natural Polymer Gelatin 20~50% in distilled water.Crosslinkable by glutaraldehyde, BDDE, or methacrylate. Collagen 1~10%in water at pH <3. Crosslinkable by glutaraldehyde, BDDE, ormethacrylate. Elastin 1~10% in water at pH <3. Crosslinkable byglutaraldehyde, BDDE, or methacrylate. Hyaluronic Acid 10~50% indistilled water. Crosslinkable by BDDE. Chondroitin sulfate 20~50% indistilled water. Crosslinkable by BDDE. Dextran 20~50% in distilledwater. Crosslinkable by BDDE Chitosan 10~20% in water at pH >8.Crosslinkable by glutaraldehyde. Alginate 5~10% in water. Crosslinkableby calcium diffusion. Heparin/Heparin 10~20% in water. Crosslinkable byBDDE. Sulfate Synthetic Polymer Polyethylene glycol, 10~95% in distillwater. Crosslinkable by amine functionalized glutaraldehyde, BDDE, ormethacrylate. Polyethylene glycol, 10~90% in distill water.Crosslinkable by hydroxyl BDDE. functionalized Polycaprolactone 65° C.,cooled to room temperature (RT) when done. Polylactic Acid ~150° C.,cooled to RT when done. Polyglycolic acid ~230° C., cooled to RT whendone. Polylactic-glycolic ~200° C., cooled to RT when done. acidCoolmorph ® 45° C., cooled to RT when done. (nondisclosed ingredients)Teflon ~300° C., cooled to RT when done. Nylon >150° C., cooled to RTwhen done. Polycarbonate ~150° C., cooled to RT when done.Polyamide >150° C., cooled to RT when done. Polystyrene ~240° C., cooledto RT when done. Inorganic Material Gold 1064° C. (m.p.) ± 200° C.,cooled to RT when done. Silver 962° C. (m.p.) ± 200° C., cooled to RTwhen done. Copper 1085° C. (m.p.) ± 200° C., cooled to RT when done.Iron 1538° C. (m.p.) ± 200° C., cooled to RT when done. Zinc 420° C.(m.p.) ± 200° C., cooled to RT when done. Nickel 1455° C. (m.p.) ± 200°C., cooled to RT when done. Cobalt 1495° C. (m.p.) ± 200° C., cooled toRT when done. Manganese 1246° C. (m.p.) ± 200° C., cooled to RT whendone. Chromium 1907° C. (m.p.) ± 200° C., cooled to RT when done.Titanium 1668° C. (m.p.) ± 200° C., cooled to RT when done. Palladium1772° C. (m.p.) ± 200° C., cooled to RT when done.

The sheath material for stretch-and-fold method is not limited to PCL,but may include any material that is capable of shaping the corecompartment into a thin filament via the stretch and fold method, and isremovable by solvent leaching, chemical erosion, or any type oftreatment that leaves the core material intact.

The sheath can be formed by one material or by a mixture of materialsfrom the following list. For precursor sheath made of a thermoplasticmaterial, the precursor will be heated above the glass transitiontemperature of the sheath material(s), at which the precursor becomesplastic and deformable. Upon the end of stretch-and-fold procedure, theprecursor will be rapidly cooled below the glass transition temperatureand solidified, which arrests Rayleigh-Plateau instability and maintainsthe core's continuity.

For precursor sheath made of a pseudoplastic material, stretched andfolded precursors may present non-Newtonian behaviors that preventRayleigh-Plateau instability and maintain the filament-shape of thecore.

For precursor sheath made of an inorganic material, the precursor willbe heated above the softening temperature of the material beforestretching and folding, and cooled below the softening temperature afterstretching and folding.

Sheath Material Conditions for Stretch Removal (Solvent or CategoryMaterial and Fold Procedure Erosion Chemical) ThermoplasticPolycaprolactone ~65° C. Acetone Coolmorph ® (non-disclosed ~45° C.Acetone ingredients) Acrylonitrile butadiene ~105° C. Acetone styreneNylon ~150° C. Trifluoroacetic acid Polyetherether ketone ~340° C.4-chlorophenol Polylactic acid ~150° C. TetrahydrofuranPolybenzimidazole >400° C. Dimethylacetamide Polycarbonate ~150° C.Dimethylformamide Polyetherimide ~200° C. N-methylpyrrolidonePolyethylene ~120° C. Acetone Poly (methyl methacrylate) 100 to 160° C.Dimethylformamide Dimethylformamide Polyethersulfone ~200° C.N-methylpyrrolidone Polyphenylene sulfide ~220° C. N-methylpyrrolidonePolystyrene ~240° C. Acetone Polyvinyl chloride 100 to 260° C.Tetrahydrofuran Polysulfone ~190° C. N-methylpyrrolidone Polyamide >150°C. Trifluoroacetic acid Polyacrylonitrile ~320° C. DimethylformamidePolyethylene terephthalate ~250° C. - Hexafluoro-2- PseudoplasticSucrose (95~99% in water) Room Water Compound temperature ~60° C. Clay(mixture of solid Room Water particles and water) temperature ~60° C.Polymer Clay (mixture of Room Tetrahydrofuran solid particles andpolymers) temperature ~60° C. Gum base (mixture of solid RoomTetrahydrofuran particles and plastic temperature ~60° C. polymers)Inorganic Borosilicate Softening point Hydrofluoric Acid Material740~990° C. (Suitable for Quartz Softening point Hydrofluoric Acidmetallic cores) 1530~1720° C.

Besides a ring, the precursor 100 can have any shape that can bestretched and folded, such as a rod or a plate (FIG. 7A).

The core 102 of the precursor 100 may have alternative cross-sections,such that the resulting micro/nanofibers may inherit differentcross-sections (FIG. 7B). Possible geometries for the cross-sectionsinclude (but are not limited by) square, triangle, rectangle, semicircle, diamond, hexagon, pentagon, and octagon. The core materials canbe divided into two or more compartments that contain differentmaterials, such that the micro/nanofibers may become composite fibers(FIG. 7C). Materials in the compartments may be selected to promotecharge-separation, redox reaction, and plasmon resonance, which mayfacilitate the functions of energy, electronics and optical devices.Possible geometries for the compartments include (but are not limitedby) co-axis cylinders, co-axis polygon, bi-layered beam, and radiallyorganized compartments.

The above embodiments were demonstrated by hand operations. However, anautomatic system capable of conducting the stretching and folding cycleswould be highly desirable for manufacturers, since the automatic systemfacilitates mass production and better provides repeatable results. Anautomatic system may also accelerate the thinning and elongation of corefiber, such that core-thinning and elongation may outpace theRayleigh-Plateau instability, and maintain fiber continuity. The designsof two Stretch-and-Fold Machines 200, 300 are shown in FIGS. 8A-11B anddescribed below.

This machine stretches and folds a pseudoplastic precursor repeatedly,and shapes the precursor into fibers. Here the precursor is shaped intoa ring. This stretch-and-fold machine is described as below:

The machine 200 has three main components (FIGS. 8A-8C):

(1) A cone 202, which stretches the bulk-material ring by pushing thematerial down the slope of the cone 202.

(2) A mechanical iris 204 is motorized to open/close its aperture 206and also to move up/down, which enables the iris 204 to push the ring100 down the cone 202 (FIG. 8A), lift the ring 100 up from the cone 202(FIG. 8B), and transfer the ring 100 from the cone 202 to a pair offlipping arms 210, 212 (FIG. 8C).

(3) Flipping arms 210, 212 are designed to catch the ring 100 from theiris 204, fold the ring 100, and release the ring 100 back to the cone202. One of the arms 210 moves linearly and rotates axially, and theother arm 212 moves linearly and bends up/down (FIG. 8C).

The stretch-and-fold machine 200 functions as follows:

Step 1: Load the Ring. The precursor ring 100 is positioned on the cone202.

Step 2: Stretch the Ring. To stretch the ring 100, the iris 204 ispositioned right above the ring 100 on the cone 202. The iris 204 movesdown while opening the aperture 206 gradually, such that the diameter ofaperture 206 matches the diameter of cone 202. The iris 204 pushes thering 100 down the cone 202 by the edge of aperture 206, while stretchingthe ring 100 via the slope of cone 202 (FIG. 8A).

Step 3: Lift the Ring from the Cone. The following steps lift the ring100 up from the cone 202. (a) The iris aperture 206 opens further andbecomes wider than the stretched ring 100. (b) The iris 204 moves down,passing the ring 100. (c) The iris aperture 206 closes and becomenarrower than the ring 100. (d) The iris 204 moves up, lifting the ring100 by the edge of aperture 206 (FIG. 8B).

Step 4: Transfer the Ring to the Flipping Arms. The following stepstransfer the ring 100 from the iris 204 to the flipping arms 210, 212.(a) The arms 210, 212 approach each other and standby underneath theiris 204. (b) The iris 204 opens the aperture 206 and drops the ring 100onto the flipping arms 210, 212 (FIG. 8C).

Step 5: Fold the Ring (FIG. 8C). (a) One flipping arm 212 rotatesaxially by 180 degrees (FIG. 8D), twisting the ring 100 into adouble-ring, while dropping one side of the double ring 100 onto to thecone 202 (FIG. 8E). (b) The arms 210, 212 move another side of thedouble ring 100 to above the cone 202. The arm 210 that is holding thering 100 bends downward and releases the side of the double-ring ontothe cone 202 (FIG. 8F).

Repeat Step 2 to Step 5 until the desired core diameter is achieved(Each cycle doubles the length of the core 102, and decreases thediameter of the core 102 by √2 each time).

Stretch-and-Fold Machine 300 is shown in FIGS. 9A-9G. Similar theprevious stretch-and-fold machine 200, this machine 300 stretches andfolds a precursor repeatedly and turns the precursor into a fiber.However, here the precursor is shaped into a rod 150 instead of a ring.The stretch-and-fold machine 300 is described as follows:

The machine 300 has the following components (FIG. 9A).

(1) A gripper base 302. The base 302 supports four Grippers 1-4; eachhas a pair of gripping tips 304. The grippers 1-4 are positioned aroundthe center of gripper base 302, by 90° angular spacing. Each gripper 1-4faces toward the center. To help explanation, two opposing grippers arelabeled “gripper 1” and “gripper 2”. The other two opposing grippers arelabeled “gripper 3” and “gripper 4”. The grippers are motorized forthree types of motions:

-   -   (i) Grasps or releases the precursor rod 150 by opening or        closing the gripping tips 304.    -   (ii) Rotates axially.    -   (iii) Approaching or withdrawing from the center.

(2) A gripper base driver (not shown). The gripper base is motorized torotate, such that opposing grippers (grippers 1 & 2 or grippers 3 & 4)are oriented to face a specific direction. This direction is eitherperpendicular to or in parallel with the direction of gravity.

The stretch-and-fold machine 300 operates as follows:

Step 1: Load the Rod 150. Gripper 1 and 2 grasp the precursor rod 150 byends 152, 154. (FIG. 9B).

Step 2: Stretch the Rod 150. Gripper 1 and 2 stretch the rod 150 bywithdrawing from each other (FIG. 9C).

Step 3: Fold the Rod 150. The gripper base re-orients gripper 1 and 2,so the rod 150 becomes horizontal. Grippers 1 and 2 approach each otherand fold the rod 150 while the gravity assists folding (FIG. 9D).

Step 4: Transfer the Rod 150 from Grippers 1&2 to Grippers 3&4. Gripper4 grasps the center 156 or rod 150 from below (FIG. 9E). The gripperbase rotates Gripper 4 to the top, turning the rod 150 up side down(FIG. 9F). Gripper 1 and 2 release the rod 150, and gripper 3 grasps therod 150 by the open ends 158, 159 from below.

Step 5: Twist the rod 150. Gripper 3 and 4 twist the rod 150 by axialrotation (FIG. 9G). Twisting helps maintain the round cross-section ofthe core.

Repeat Step 2 to Step 5: Repeatedly stretch, fold, transfer and twistthe precursor rod 150, until the desired core diameter is obtained (Eachcycle decreases the diameter of the core of rod 150 by √2 (=1.414)time).

Referring now to FIGS. 10A-10K, a machine 400 for stretching and foldingprecursor 100 and a method of using machine 400 is shown. The precursor100 is shaped into rod 150. The stretch-and-fold machine 400 contains amechanism to fold the rod 150 repeatedly, and this machine 400 resemblesa machine for producing taffy. This machine 400, however, issignificantly different from a taffy machine in two perspectives:

(1) Uniform Stretching: During each cycle, machine 400 stretches eachsection of the rod precursor 150 by a length ratio of 2.414 (=1+√2) anduniformly reduces the diameter of the core of the rod 150 by a ratio of0.586 (=1/[(1/√2)+1]). In contrast, a traditional taffy machinestretches a candy rod by different stretching ratio for differentsegments, which forms a broad distribution of fiber diameters, andcannot use used to conduct the desired stretch-and-fold protocol.

(2) Buoyancy and Heating. To help stabilize the geometry of the rodprecursor 150 during stretching and folding, the rod precursor 150 issubmersed in a liquid of the equal density of the rod 150, such that therod 150 may not be draped by gravity. Furthermore, to maintain the rod'splasticity, the liquid is heated and maintained at the meltingtemperature of the rod 150 (>65° C.). The liquid is a sucrose solution,prepared by mixing water and cane sugar at a weight ratio of 2:1. Thesucrose solution is heated and maintained at 70° C. using an isothermalwater bath.

The machine 400 has the following components

(1) A gripper base 402 (FIGS. 10A-10B). The base 402 supports fourgrippers 1-4. The grippers 1-4 are positioned around the center ofgripper base 402, by 90° angular spacing. Each gripper 1-4 is supportedby an arm 410 extending toward the center. Each arm 410 is motorized andmoves by two degrees of freedom. The rod precursor 150 is fixed togripping tips 412 at the end of each arm 410, and the arms 410 performthe stretch-and-fold routine by the following motions: (a) Rotationabout the z-axis. (b) Rotation about the axis of the arm 410. To helpthe following explanation, here two opposing grippers are labeled“gripper 1” and “gripper 2”. The other pair are labeled “gripper 3” and“gripper 4”.

(2) An isothermal water bath 420 (FIG. 10C). The water bath 420 containsthe above 70° C. sucrose water solution, and the grippers 1-4 aresubmersed in the sucrose solution, which maintain the temperature of therod 150 above its melting point.

The stretch-and-fold machine 400 operates as follows:

Step 1: Load the Rod 150. Gripper 1 and 2 grasp the precursor rod 150 byends 152, 154. (FIG. 10D).

Step 2: Twist the Rod 150. Following arm motions, Gripper 3 and Gripper4 approach the mid section of the rod 150, such that Grippers 1, 2, 3and 4 align with each other in a straight line and all grippers 1-4 griprod 150. Afterward, Gripper 3 and Gripper 4 rotate about this straightline by 180 degrees, which twists the mid section of the rod 150 by 180degrees while securing the rod 150 to Gripper 3 and Gripper 4 (FIG.10E).

Step 3: Stretch the Rod 150. Grippers 3 and Gripper 4 return to theiroriginal position. This motion pulls the rod into a “Z” shape, extendingthe overall length of the rod 150 by 2.414 (=1+√2) folds, and decreasesthe diameter of the precursor core (which forms the fibers) by a ratioof 0.586 (=1/[(1/√2)+1]). (FIG. 10F to 10G).

Step 4: Fold and Twist the Rod 150. Gripper 1 and Gripper 2 approach themid section of the rod 150, such that Grippers 1, 2, 3 and 4 align witheach other in a straight line and all grippers 1-4 grip rod 150. Thismotion folds the rod 150, while turning the shape of the precursor from“Z” shape back to a rod shape. Afterward, Gripper 1 and Gripper 2 rotateabout this straight line by 180 degrees, which twists the mid section ofthe rod by 180 degrees while securing the rod to Gripper 1 and Gripper 2(FIG. 10G to 10I).

Step 4: Stretch the Rod 150 Again. Grippers 1 and Gripper 2 return totheir original position. This motion pulls the rod 150 into a “Z” shapeand extends the overall length of the rod by 2.414 (=1+√2) folds, anddecreases the diameter of the precursor core (which forms the fibers) bya ratio of 0.586 (=1/[(1/√2)+1]) (FIGS. 10I to 10J).

Step 5: Fold and Twist the Rod 150 Again. Gripper 3 and Gripper 4approach the mid section of the rod 150, such that Grippers 1, 2, 3 and4 align with each other in a straight line and all grippers 1-4 grip rod150. This motion folds the rod, while turning the shape of the precursorfrom “Z” shape back to a rod shape. Afterward, Gripper 3 and Gripper 3rotate about this straight line by 180 degrees, which twists the midsection of the rod 150 by 180 degrees while securing the rod to Gripper3 and Gripper 4 (FIG. 10J to 10K, then back to 10F).

Repeat Step 3 to Step 5: Repeatedly stretch, fold, and twist the rod 150precursor until the desired core diameter is obtained.

The above machines 300-400 are examples for the automation ofStretch-and-Fold method. However, these examples should not be used tolimit the scope of this automatic system. For example, the iris 202 forstretching a ring-shaped precursor 100 can be replaced by theumbrella-like mechanisms in machine 500 in FIGS. 11A-11B.

The nature of the automatic system is therefore much broader than theabove embodiments, and should be based on the following description:

(1) An automatic machine 500 to stretch and fold a precursor 100 made ofa bulk material, which has a specific shape, and to transform the bulkmaterial into a filament, the filament diameter is adjustable from 10nanometers to 1 millimeter. The machine 500 performs the followingfunctions:

-   -   a. A stretching function, which elongates and thins the        precursor 100.    -   b. A folding function, which folds the precursor 100.    -   c. A transferring function, which transfers the precursor 100        between the stretching function and the folding function.

(2) In (1), the precursor 100 has an initial shape of a ring, acylinder, an ellipsoid, a sphere, a cube, a cuboid, a cone, ahemisphere, a polygonal prism such as triangular prism, rectangularprism, pentagonal prism, or hexagonal prism, or a polygonal pyramid suchas triangle based pyramid, square based pyramid, pentagon based pyramid,or hexagon based pyramid.

(3) In (1), the precursor 100 contains core 102 and sheath 104 asdescribed above. The sheath 104 keeps the core 102 separated during thefolding and stretching, and is removable for releasing the core 102. Thecore 102 has an initial shape of a ring, a cylinder, an ellipsoid, asphere, a cube, a cuboid, a cone, a hemisphere, a polygonal prism suchas triangular prism, rectangular prism, pentagonal prism, or hexagonalprism, or a polygonal pyramid such as triangle based pyramid, squarebased pyramid, pentagon based pyramid, or hexagon based pyramid.

(4) In (3), the sheath 104 can be removed by a solvent, such that thecore 102 after stretching and folding is releasable by solvent leaching.

(5) In (1), the stretching function is performed by a stretching module.The stretching module contains a motor and at least one holder, in whichthe motor actuates the holder to stretch the precursor.

(6) In (5), the holder contains a cone 202 and a mechanical iris 204.The iris 204 pushes the precursor 100 along the cone 202, therebystretching the precursor 100 by the slope of the cone 202.

(7) In (5), the holder contains a pair of grippers 1, 2 holding theprecursors 150. The grippers 1, 2 stretch the precursor 150 bywithdrawing from each other.

(8) In (1), the folding function is performed by a folding module thatcontains one motor and at least one gripper. The motor actuates thegripper to fold the bulk material.

(9) In (8), the folding module includes a hanger and a pair of grippersholding the precursor 150. The grippers 110, 112 fold the precursor 150by twisting the precursor 150 on the hanger, which supports theprecursor 150.

(10) In (9), the hanger is a cone 202, and the precursor 100 isring-shaped.

(11) In (8), the folding module includes a pair of grippers 1, 2 holdingthe precursor 150. The grippers 1, 2 fold the precursor 150 byapproaching each other.

(12) In (1), the stretching function is performed by a cone 202 and amechanical iris 204. The iris 204 pushes the precursor 100 along thecone 202, thereby stretching the precursor 100 by the slope of the cone202; the folding function is performed by a pair of grippers 110, 112holding the precursor 100, the grippers 110, 112 fold the precursor 100by twisting the precursor 100 upon the cone 202; the transferringfunction is performed by the cone 202 and iris 204; the cone 202supports the precursor 100 upon stretching and after folding; the iris204 lifts the precursor 100 from the cone 202 after stretching, andreleases the precursor 100 to the grippers 110, 112 before folding.

(13) In (1), the stretching and folding function are performed by a pairof first grippers 1, 2 holding the precursor 150; the first grippers 1,2 stretch the precursor 150 by withdrawing from each other, and fold theprecursor 150 by approaching each other; the transferring function isperformed by a pair of second grippers 3, 4; the second grippers 3, 4grasp the precursor 150 from the first grippers 1, 2 after folding. Thefunctions of the first and second grippers 1, 2, and 3, 4 swap aftereach stretching and folding cycle.

(14) In (1) the system includes a thermal module 420. The module 420maintains the precursor's temperature above a plastic temperature, atwhich the precursor 150 becomes plastic.

The stretch-and-fold technology described herein has shown the followingadvantages for mass-production:

Arrested Rayleigh Instability. Made of a high molecular weightthermoplastic, the sheath 104 provides high viscosity in the meltedphase (u>1×10⁶ cP-s). This delays the Rayleigh instability and maintainsthe gelatin core 102 by minutes beyond the stretch/fold cycles. TheRayleigh instability is arrested by cooling the sheath 104 to the solidphase after the stretching and folding.

High Production Rate and Easily Tunable Diameter. Following the powerlaw, the number of microfibers (n) increases exponentially with thenumber of stretch/fold cycles (n=2^(N)), while the fiber diameterdecreases exponentially with the cycles (D=D₀/2^(0.5N)), which enablesan easy customization of fiber diameter. In experiments, the smallestdiameter achieved was about 200 nm. The production rate of microfiberswas constantly high regardless of the change in diameter and the totalweight of the microfibers. For example, after 25 stretch/fold cycles and2 min, a 1-gram gelatin core of 3 mm initial diameter was turned into abundle of 33,554,432 microfibers of 0.52±0.08 μm (=520±80 nm) diameter.Increasing the yield of the 520 nm microfibers by 16-fold spent fourextra cycles, or 0.5 other minutes. In contrast, the fabrication time ofthe conventional fibers spinning often linearly increases with theyield. See the graph of FIG. 12.

The success of stretch-and-fold method relies on the delay of Rayleighinstability. Increasing the number of stretch-and-fold cyclesunlimitedly will eventually induce instability, breaking the corebiopolymers into micro/nano-beads. However, the inventors havediscovered that the instability could be out-paced, and microfibers 520nm in diameter can be produced from gelatin via 25 stretch-and-foldcycles when the following conditions are met:

(1) High-molecular-weight (˜50,000 Da) polycaprolactone for thethermoplastic sheath.

(2) 300-boom porcine gelatin for the core polymer.

(3) Conduct the process at a lower temperature slightly above themelting point of the sheath (˜60 degrees C.).

(4) Complete all cycles in 3 min. Cool the sheath material to roomtemperature, solidifying the sheath

The achievable minimum diameter became 15-20 μm when the overall cyclingtime became 20 minutes. The minimum diameter became 1-2 μm when thetemperature was raised to 80 degrees C. The minimum diameter became 2-4μm when using a sheath polymer of lower molecular weight (about 10,000Da).

The arrest of Rayleigh Instability can be modeled mathematically. Thecore of polymer solution was modeled, which is in a bundle of identicalcores of polymer solution, as a cylinder of a viscous liquid surroundedby a cylindrical sheath made of another viscous liquid. The corecylinder has a radius of a, and the sheath cylinder has an externalradius of b. Assuming that the fluid flow is symmetric about the centralaxis of the core cylinder, the dynamics equations of the liquids ofviscosity μ and density ρ, respectively, are:

$\begin{matrix}{\left. \begin{matrix}\begin{matrix}{{\rho\left( {\begin{matrix}{\partial u} \\{\partial t}\end{matrix} + {u\begin{matrix}{\partial u} \\{\partial r}\end{matrix}} + {w\begin{matrix}{\partial u} \\{\partial z}\end{matrix}}} \right)} = {{- \begin{matrix}{\partial p} \\{\partial r}\end{matrix}} +}} \\{\mu\left( {\begin{matrix}{\partial^{2}u} \\{\partial r}\end{matrix} + {\begin{matrix}1 \\r\end{matrix}\begin{matrix}{\partial u} \\{\partial r}\end{matrix}} - \begin{matrix}u \\r^{2}\end{matrix} + \begin{matrix}{\partial^{2}u} \\{\partial z^{2}}\end{matrix}} \right)}\end{matrix} \\\begin{matrix}{{\rho\left( {\frac{\partial w}{\partial t} + {u\frac{\partial w}{\partial r}} + {w\frac{\partial w}{\partial z}}} \right)} = {{- \frac{\partial p}{\partial z}} +}} \\{\mu\left( {\frac{\partial^{2}w}{\partial r^{2}} + {\frac{1}{r}\frac{\partial w}{\partial r}} + \frac{\partial^{2}w}{\partial z^{2}}} \right)}\end{matrix}\end{matrix} \right\}\quad} & {{Equation}\mspace{14mu} 1} \\{{u = {\begin{matrix}1 \\r\end{matrix}\begin{matrix}{\partial v} \\{\partial z}\end{matrix}}},{w = {{- \begin{matrix}1 \\r\end{matrix}}\begin{matrix}{\partial p} \\{\partial r}\end{matrix}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$where w and u are the axial and radial component of the fluid velocity.Equation 1 is based on the requirement of momentum conservation.Equation 2 yields the fluid velocity w and u via the Stokes streamfunction ψ, which automatically satisfies the requirement of masscontinuity. Under a disturbance with a spatial wavelength λ=2n/k, thefunction ψ becomes:Ψ=ϕ(r,z)e ^(i(nt+kz))  Equation 3and has the general solution as below:

$\begin{matrix}{{\Psi = {\left\lbrack {{A_{1}{{rI}_{1}({kr})}} + {B_{1}{{rK}_{1}({kr})}} + {A_{2}{{rI}_{1}\left( {k_{1}r} \right)}} + {B_{2}{{rK}_{1}\left( {k_{1}r} \right)}}} \right\rbrack e^{i{({{nt} + {kz}})}}}},{{{where}\mspace{14mu} k_{1}} = {\sqrt{k^{2} + \frac{{in}\;\rho}{\mu}}\quad}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

In which I_(x) and K_(x) are the modified Bessel functions of the firstand second kind. The value of n is a function of k and determines theinstability of the liquids; if the value of i*n is real and positive,the core cylinder will become varicose and dissociate over time.Therefore, the k producing the maximum i*n value determines the mostlikely spatial periodicity by which the fluid cylinder will break apart.The coefficients A_(1,2) and B_(1,2) for the stream function w arecalculated by the boundary conditions.

The boundary conditions are defined as follows:

(i) The flow velocity is finite at the center of the core.

(ii) There is no slipping at the interface of the core and sheath flow.

(iii) The tangential stress parallel to the interface of the core andsheath flow is continuous.

(iv) The difference in the normal stress between the inside and outsideof the core equals the interfacial surface tension between the core andsheath liquids.

(v) The flow velocity at the external boundary is zero.

In (v), it is assumed that there is negligible flow at the externalboundary of the sheath, due to the extremely high viscosity of thesheath liquid, and also due to the hindrance by the surrounding sheathcylinder, as shown in FIG. 13. The boundary conditions (i) leads toB′₁=B′₂=0 since K_(x) is infinite at r=0. The rest of the boundaryconditions lead to a complex 6-by-6 linear equation:M(k,n)[A ₁ A ₂ B ₁ B ₂ A ₁ ′A ₁′]^(T)=0  Equation 5

Where M(k,n) is a square matrix with 6-by-6 functions of k and n. Theexistence of non-zero (non-trivial) solution for ψ demands a zerodeterminant of M and therefore the relation between k and n:|M(k,n)|=0  Equation 6

The stream function ψ and thus the fluid flows was solved using theequations (6), (5), (4) and (2). The above theoretical modeling enablesthe prediction of how long a core of fiber will maintain cylindrical,and most importantly, how thin the fibers can become under certainfabrication conditions. Such knowledge can accelerate the design andmanufacturing of biopolymer microfibers of different diameters andpolymer properties.

Experiment: How Cell-scale 3D Topography Affects Mesenchymal Stem CellMechanotransduction.

In 2D models, cell-scale topography is known for regulatingmechanotransduction and the cell sensing of matrix elasticity. However,whether or how this phenomenon takes place in 3D is unclear. The goal ofthis experiment was to answer this question by conducting acomprehensive experimental study. Of particular focus were thecombinatory effects of porosity, and matrix anisotropicity on the stemcells differentiation of stem cells. The crosslinkable microfibers,mass-produced by the stretch-and-fold method, were used as the buildingblocks to customize pore size and matrix anisotropicity by changing thediameter and alignment of microfibers, respectively. Although stem cellsalso respond to biopolymer type, to focus on the effects of biophysicalfactors, all microfibers for our experiment was fabricated by gelatin,which is a standard biopolymer for cells culturing.

Cytoskeleton-based Mechanotransduction. Mechanotransduction in responseto matrix elasticity and topography involves the chain reactions (orsignaling pathways) among the matrix-binding proteins, e.g. integrin(FIG. 14e at f), the focal-adhesion proteins assembly (FIG. 14e at g),and the cytoskeletons between the matrix-binding proteins and the cellnuclei (FIG. 14e at h). The cytoskeletons generate tension and induceconformational change to the associated proteins, e.g. vinculin, whichexposes hidden molecules binding-sites in the proteins, which in turnfeedback to the focal adhesion assembly, which increases thecytoskeletons and forms stress fibers that produce the maximum tensionand change the cell shape. In 2D, the above pathway is hindered when thereorganization of cytoskeletons is inhibited, either by an extremelysoft matrix (<10 kPa), which does not maintain cell tension, or by avery narrow space that confines the cell shape and the cellular tension.The cell-sized microfibers created by the inventive stretch-and-foldingmethods can be applied to controlling the mechanosensing of cells in twoways. The first way is by tuning the spatial confinement of cells byselecting the fiber diameter (FIG. 7b,d ). The second way is by tuningthe elongation of cells by controlling the alignment of microfibers(FIG. 7a,c ). In general, thicker fibers form bigger pores and less cellconfinement, while thinner fibers form smaller pores and more cellconfinement. Aligned fibers often lead to elongated cell morphology,while randomized fibers promote randomly spread cell shapes.

Role of Yes Associated Proteins (YAP) in the Mechanotransduction

Through unidentified mechanisms, the activation of the above signalingnetwork activates the expression of some genes and inhibits the others,while activating the Yes Associated Protein (YAP) (FIG. 14e at i). TheYAP is a gene transcription cofactor that is involved in stem cellproliferation and differentiation into certain types of cells, such asbone cells (osteogenesis). The activated YAP proteins accumulate insidethe cell nuclei, whereas the YAP proteins that are de-activated areconfined to the cytosol, which happens when the above signaling pathwayis off. Therefore, the average location of YAP in the cells can be usedto monitor the activation of mechanotransduction of stem cells. It hasbeen shown that the activating YAP activates fibroblast and inducesscarring, while the deactivating YAP stabilizes the gene expression ofchondrocytes, which are cell types close to the meniscus cells.

Preparing Microfibers. Crosslinkable microfibers of varying diameter(0.5 μm 50 μm) were fabricated using the stretch-and-fold protocols.

Preparing MSC. Human MSC were purchased at passage-2. The cells werecounted and seeded onto tissue culture flasks with Dulbecco's modifiedEagle medium (DMEM), containing fetal bovine serum (FBS) (10%) andantibiotic penicillin/streptomycin (P/S) solution (1%). Following theinitial 48 hr of incubation at 37° C. and 5% CO₂, cells were washed withPBS and expanded in DMEM with 10% FBS, 1% P/S and 10 ng/mL basicfibroblast growth factor. The cells were passaged upon 85-90% confluenceand passage-5 cells will be used for all experiments.

Fabricate Cellularized Scaffolds of Customized Pore Sizes andAnisotropicity. Microfibers were rehydrated by 10 wt % density. Toprepare anisotropic scaffolds, aligned microfibers were gentlyfold-mixed with MSC to reach 5 million/mL uniform cell density, whilekeeping the direction of folding perpendicular to the fiber alignment.The microfibers were molded, photo-crosslinked into 2 mm thick scaffoldsand incubated in the MSC culture medium. To prepare isotropic scaffolds,the above procedure was repeated using randomized microfibers withoutalignment. Cell viability was examined after 48 hr with live/deadreagents (Thermo Fisher). The porosity of microfibers was tuned between2 μm and 200 μm by the selected of microfiber diameters (0.5 μm 50 μm).The morphology of resulting scaffolds was evaluated using SEM.

Analyze the Mechanosensing of Stem Cells. The results, shown in FIG. 15,demonstrated that pore-size and anisotropicity significantly impact thecell morphology. Samples were harvested 14 days post-cultured and werefixed and cryo-sectioned. All samples were immunostained for YAP and thecytoskeleton components including vinculin, α-tubulin, andphosphorylated focal adhesion kinase (pFAK), followed bycounter-staining for the stress fibers (phalloidin) and cell nuclei. Theimmunostained samples were imaged in 3D by confocal microscopy. Imageprocessing was performed using program ImageJ (National institute ofHealth). 3D cell structures were reconstructed from confocal imagestacks, and the cell morphology was be characterized by cell length,aspect ratio, volume, and cell-cell alignment (FIGS. 15a-h ). Celltension was be estimated by the distribution and signal intensity ofvinculin, pFAK, and stress-fibers. The status of mechanotransduction wascharacterized by the distribution of YAP inside or outside the cellnuclei (FIG. 15i .). Correlation among scaffold properties and cellproperties was analyzed by using Excel and MATLAB programming.

MSC encapsulated among thin fibers (which gave sub-cellular size pores)had round morphology and significantly lower amount of YAP presented inthe cell nuclei (FIGS. 15a, 15b ). In contrast, MSC encapsulated amongthe thick fibers (which gave pores larger than the cells) hadwide-spreading morphology and significantly higher amount of YAPpresented in the cell nuclei (FIGS. 15c, 15d ). Interestingly, when thethin fibers were used but aligned into a linear formation, the YAP inthe MSC nuclei became significantly higher than the MSC among the thinfibers that were randomized (FIGS. 15e, 15f vs. 15, 15 b). The resultsdemonstrated that the alignment and diameter of the stretched-and-foldedfibers significantly impacted the mechanosensing of stem cells, whichmakes these fibers highly promising for the clinical applications wherethe stem cells' fate needed to be controlled.

While the above-described methods for forming micro-fibers andnano-fibers are performed using machinery, those skilled in the art willrecognize that at least some of the methods described above can beperformed manually, in the absence of any machinery.

It will be further understood that various changes in the details,materials, and arrangements of the parts which have been described andillustrated in order to explain the nature of this invention may be madeby those skilled in the art without departing from the scope of theinvention as expressed in the following claims.

The invention claimed is:
 1. A method for producing microfiberscomprising the steps of: (a) providing a base material; (b) forming thebase material in a ring; (c) gripping opposing ends of the ring; (d)flipping one of the opposing ends relative to the other of the opposingends, forming an upper portion and a lower portion; (e) folding theupper portion onto the lower portion; (f) stretching the folded upperand lower portions; and (g) repeating steps (d)-(f) as desired.
 2. Themethod according to claim 1, wherein steps (d)-(f) are performedsufficient times to form fibers with sub-micron diameter.
 3. The methodaccording to claim 1, wherein step (a) comprises providing aprotein-based base material.
 4. The method according to claim 1, whereinstep (a) comprises providing a sheath around the base material.
 5. Themethod according to claim 4, wherein the method further comprises thestep of: (h) dissolving the sheath.
 6. The method according to claim 1,wherein the method is performed manually.
 7. The method according toclaim 1, wherein the method is performed automatically.
 8. The methodaccording to claim 7, wherein the method comprises providing a machine,wherein the machine performs steps (c)-(g).
 9. The method according toclaim 8, wherein step (f) comprises forcing the folded upper and lowerportions onto a cone.
 10. The method according to claim 8, wherein step(f) comprises placing the folded upper and lower portions around a frameand expanding the frame.
 11. The method according to claim 10, whereinthe frame comprises a plurality of radially expanding posts.
 12. Themethod according to claim 10, wherein the frame comprises a radiallyexpanding bladder.